TSTP Solution File: SCT089-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SCT089-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Mon Jul 18 22:03:50 EDT 2022
% Result : Unsatisfiable 5.57s 5.89s
% Output : Refutation 5.57s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SCT089-1 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.35 % Computer : n008.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Fri Jul 1 23:18:38 EDT 2022
% 0.13/0.35 % CPUTime :
% 1.09/1.49 ============================== Prover9 ===============================
% 1.09/1.49 Prover9 (32) version 2009-11A, November 2009.
% 1.09/1.49 Process 27039 was started by sandbox on n008.cluster.edu,
% 1.09/1.49 Fri Jul 1 23:18:39 2022
% 1.09/1.49 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_26884_n008.cluster.edu".
% 1.09/1.49 ============================== end of head ===========================
% 1.09/1.49
% 1.09/1.49 ============================== INPUT =================================
% 1.09/1.49
% 1.09/1.49 % Reading from file /tmp/Prover9_26884_n008.cluster.edu
% 1.09/1.49
% 1.09/1.49 set(prolog_style_variables).
% 1.09/1.49 set(auto2).
% 1.09/1.49 % set(auto2) -> set(auto).
% 1.09/1.49 % set(auto) -> set(auto_inference).
% 1.09/1.49 % set(auto) -> set(auto_setup).
% 1.09/1.49 % set(auto_setup) -> set(predicate_elim).
% 1.09/1.49 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.09/1.49 % set(auto) -> set(auto_limits).
% 1.09/1.49 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.09/1.49 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.09/1.49 % set(auto) -> set(auto_denials).
% 1.09/1.49 % set(auto) -> set(auto_process).
% 1.09/1.49 % set(auto2) -> assign(new_constants, 1).
% 1.09/1.49 % set(auto2) -> assign(fold_denial_max, 3).
% 1.09/1.49 % set(auto2) -> assign(max_weight, "200.000").
% 1.09/1.49 % set(auto2) -> assign(max_hours, 1).
% 1.09/1.49 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.09/1.49 % set(auto2) -> assign(max_seconds, 0).
% 1.09/1.49 % set(auto2) -> assign(max_minutes, 5).
% 1.09/1.49 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.09/1.49 % set(auto2) -> set(sort_initial_sos).
% 1.09/1.49 % set(auto2) -> assign(sos_limit, -1).
% 1.09/1.49 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.09/1.49 % set(auto2) -> assign(max_megs, 400).
% 1.09/1.49 % set(auto2) -> assign(stats, some).
% 1.09/1.49 % set(auto2) -> clear(echo_input).
% 1.09/1.49 % set(auto2) -> set(quiet).
% 1.09/1.49 % set(auto2) -> clear(print_initial_clauses).
% 1.09/1.49 % set(auto2) -> clear(print_given).
% 1.09/1.49 assign(lrs_ticks,-1).
% 1.09/1.49 assign(sos_limit,10000).
% 1.09/1.49 assign(order,kbo).
% 1.09/1.49 set(lex_order_vars).
% 1.09/1.49 clear(print_given).
% 1.09/1.49
% 1.09/1.49 % formulas(sos). % not echoed (813 formulas)
% 1.09/1.49
% 1.09/1.49 ============================== end of input ==========================
% 1.09/1.49
% 1.09/1.49 % From the command line: assign(max_seconds, 300).
% 1.09/1.49
% 1.09/1.49 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.09/1.49
% 1.09/1.49 % Formulas that are not ordinary clauses:
% 1.09/1.49
% 1.09/1.49 ============================== end of process non-clausal formulas ===
% 1.09/1.49
% 1.09/1.49 ============================== PROCESS INITIAL CLAUSES ===============
% 1.09/1.49
% 1.09/1.49 ============================== PREDICATE ELIMINATION =================
% 1.09/1.49 1 class_Ring__and__Field_Ocomm__semiring__1(tc_nat) # label(clsarity_nat__Ring__and__Field_Ocomm__semiring__1) # label(axiom). [assumption].
% 1.09/1.49 2 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) # label(cls_class__semiring_Oadd__a_0) # label(axiom). [assumption].
% 1.09/1.49 3 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) # label(cls_class__semiring_Osemiring__rules_I25_J_0) # label(axiom). [assumption].
% 1.09/1.49 4 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)),C) # label(cls_class__semiring_Osemiring__rules_I23_J_0) # label(axiom). [assumption].
% 1.09/1.49 5 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)) # label(cls_class__semiring_Osemiring__rules_I22_J_0) # label(axiom). [assumption].
% 1.09/1.49 6 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) # label(cls_class__semiring_Osemiring__rules_I21_J_0) # label(axiom). [assumption].
% 1.09/1.49 7 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),B) # label(cls_class__semiring_Osemiring__rules_I24_J_0) # label(axiom). [assumption].
% 1.09/1.49 8 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),B) # label(cls_class__semiring_Oadd__c_0) # label(axiom). [assumption].
% 1.09/1.49 9 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Power_Opower__class_Opower(B,c_HOL_Oone__class_Oone(tc_nat),A) = B # label(cls_class__semiring_Osemiring__rules_I33_J_0) # label(axiom). [assumption].
% 1.09/1.49 10 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),E)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),E)) # label(cls_class__semiring_Osemiring__rules_I20_J_0) # label(axiom). [assumption].
% 1.09/1.49 11 -class_Ring__and__Field_Ono__zero__divisors(A) | -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(B,C) != c_HOL_Ozero__class_Ozero(A) | -hBOOL(hAPP(hAPP(c_in(D),C),E)) | -c_Finite__Set_Ofinite(E,D) | c_Finite__Set_Osetprod(B,E,D,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_setprod__zero__iff_2) # label(axiom). [assumption].
% 1.09/1.49 12 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(B,C) != c_HOL_Ozero__class_Ozero(A) | -hBOOL(hAPP(hAPP(c_in(D),C),E)) | -c_Finite__Set_Ofinite(E,D) | c_Finite__Set_Osetprod(B,E,D,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_setprod__zero_0) # label(axiom). [assumption].
% 1.09/1.49 13 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),B) = B # label(cls_class__semiring_Oadd__0_0) # label(axiom). [assumption].
% 1.09/1.49 14 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Ozero__class_Ozero(A)) = B # label(cls_class__semiring_Osemiring__rules_I6_J_0) # label(axiom). [assumption].
% 1.09/1.49 15 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),B) = B # label(cls_class__semiring_Osemiring__rules_I5_J_0) # label(axiom). [assumption].
% 1.09/1.49 16 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Power_Opower__class_Opower(B,c_HOL_Ozero__class_Ozero(tc_nat),A) = c_HOL_Oone__class_Oone(A) # label(cls_class__semiring_Opwr__0_0) # label(axiom). [assumption].
% 1.09/1.49 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),C). [resolve(1,a,2,a)].
% 1.09/1.49 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C)),B). [resolve(1,a,4,a)].
% 1.09/1.49 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C)). [resolve(1,a,5,a)].
% 1.09/1.49 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C)). [resolve(1,a,6,a)].
% 1.09/1.49 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),A). [resolve(1,a,7,a)].
% 1.09/1.49 Derived: c_Power_Opower__class_Opower(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = A. [resolve(1,a,9,a)].
% 1.09/1.49 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),D)). [resolve(1,a,10,a)].
% 1.09/1.49 Derived: -class_Ring__and__Field_Ono__zero__divisors(tc_nat) | hAPP(A,B) != c_HOL_Ozero__class_Ozero(tc_nat) | -hBOOL(hAPP(hAPP(c_in(C),B),D)) | -c_Finite__Set_Ofinite(D,C) | c_Finite__Set_Osetprod(A,D,C,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(1,a,11,b)].
% 1.09/1.52 Derived: hAPP(A,B) != c_HOL_Ozero__class_Ozero(tc_nat) | -hBOOL(hAPP(hAPP(c_in(C),B),D)) | -c_Finite__Set_Ofinite(D,C) | c_Finite__Set_Osetprod(A,D,C,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(1,a,12,a)].
% 1.09/1.52 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A) = A. [resolve(1,a,13,a)].
% 1.09/1.52 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Ozero__class_Ozero(tc_nat)) = A. [resolve(1,a,14,a)].
% 1.09/1.52 Derived: c_Power_Opower__class_Opower(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Oone__class_Oone(tc_nat). [resolve(1,a,16,a)].
% 1.09/1.52 17 class_Ring__and__Field_Oordered__semidom(tc_nat) # label(clsarity_nat__Ring__and__Field_Oordered__semidom) # label(axiom). [assumption].
% 1.09/1.52 18 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_Power_Opower__class_Opower(B,c_Suc(C),A)),c_HOL_Oone__class_Oone(A))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),c_HOL_Oone__class_Oone(A))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),B)) # label(cls_power__Suc__less__one_0) # label(axiom). [assumption].
% 1.09/1.52 19 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(hAPP(c_lessequals(A),c_Nat_Osemiring__1__class_Oof__nat(B,A)),c_Nat_Osemiring__1__class_Oof__nat(C,A))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),C)) # label(cls_of__nat__le__iff_1) # label(axiom). [assumption].
% 1.09/1.52 20 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_Nat_Osemiring__1__class_Oof__nat(B,A)),c_Nat_Osemiring__1__class_Oof__nat(C,A))) # label(cls_of__nat__le__iff_0) # label(axiom). [assumption].
% 1.09/1.52 21 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),c_Power_Opower__class_Opower(B,C,A))) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),B)) # label(cls_zero__le__power_0) # label(axiom). [assumption].
% 1.09/1.52 22 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Oone__class_Oone(A)),c_Power_Opower__class_Opower(B,C,A))) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Oone__class_Oone(A)),B)) # label(cls_one__le__power_0) # label(axiom). [assumption].
% 1.09/1.52 23 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(hAPP(c_lessequals(A),c_Power_Opower__class_Opower(B,C,A)),c_Power_Opower__class_Opower(B,D,A))) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Oone__class_Oone(A)),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),C),D)) # label(cls_power__increasing_0) # label(axiom). [assumption].
% 1.09/1.52 24 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(hAPP(c_lessequals(A),c_Power_Opower__class_Opower(B,C,A)),c_Power_Opower__class_Opower(D,C,A))) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),D)) # label(cls_power__mono_0) # label(axiom). [assumption].
% 1.09/1.52 25 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Oone__class_Oone(A)),c_Power_Opower__class_Opower(B,C,A))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Oone__class_Oone(A)),B)) # label(cls_one__less__power_0) # label(axiom). [assumption].
% 1.09/1.52 26 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_Power_Opower__class_Opower(B,C,A)),c_Power_Opower__class_Opower(D,C,A))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),D)) # label(cls_power__strict__mono_0) # label(axiom). [assumption].
% 1.09/1.52 27 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_Power_Opower__class_Opower(B,C,A)),c_Power_Opower__class_Opower(B,D,A))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),c_HOL_Oone__class_Oone(A))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),D),C)) # label(cls_power__strict__decreasing_0) # label(axiom). [assumption].
% 1.09/1.52 28 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(hAPP(c_lessequals(A),c_Power_Opower__class_Opower(B,C,A)),c_Power_Opower__class_Opower(B,D,A))) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),c_HOL_Oone__class_Oone(A))) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),D),C)) # label(cls_power__decreasing_0) # label(axiom). [assumption].
% 1.09/1.52 29 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_Power_Opower__class_Opower(B,D,A)),c_Power_Opower__class_Opower(C,D,A))) # label(cls_power__less__imp__less__base_0) # label(axiom). [assumption].
% 1.09/1.52 30 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),c_Power_Opower__class_Opower(B,C,A))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),B)) # label(cls_zero__less__power_0) # label(axiom). [assumption].
% 1.09/1.52 31 -class_Ring__and__Field_Oordered__semidom(A) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Oone__class_Oone(A)),c_HOL_Ozero__class_Ozero(A))) # label(cls_not__one__less__zero_0) # label(axiom). [assumption].
% 1.09/1.52 32 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),c_HOL_Oone__class_Oone(A))) # label(cls_zero__le__one_0) # label(axiom). [assumption].
% 1.09/1.52 33 -class_Ring__and__Field_Oordered__semidom(A) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_Nat_Osemiring__1__class_Oof__nat(B,A)),c_HOL_Ozero__class_Ozero(A))) # label(cls_of__nat__less__0__iff_0) # label(axiom). [assumption].
% 1.09/1.52 34 -class_Ring__and__Field_Oordered__semidom(A) | c_Power_Opower__class_Opower(B,C,A) != c_Power_Opower__class_Opower(D,C,A) | B = D | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),D)) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),B)) # label(cls_power__eq__imp__eq__base_0) # label(axiom). [assumption].
% 1.09/1.52 35 -class_Ring__and__Field_Oordered__semidom(A) | c_Power_Opower__class_Opower(B,c_Suc(C),A) != c_Power_Opower__class_Opower(D,c_Suc(C),A) | B = D | -hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),D)) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),B)) # label(cls_power__inject__base_0) # label(axiom). [assumption].
% 1.09/1.52 36 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Oone__class_Oone(A)),c_HOL_Oone__class_Oone(A)))) # label(cls_zero__less__two_0) # label(axiom). [assumption].
% 1.09/1.52 37 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),c_Nat_Osemiring__1__class_Oof__nat(B,A))) # label(cls_of__nat__0__le__iff_0) # label(axiom). [assumption].
% 1.09/1.52 38 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),c_Nat_Osemiring__1__class_Oof__nat(B,A))) # label(cls_zero__le__imp__of__nat_0) # label(axiom). [assumption].
% 1.09/1.52 39 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_Power_Opower__class_Opower(D,B,A)),c_Power_Opower__class_Opower(D,C,A))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Oone__class_Oone(A)),D)) # label(cls_power__le__imp__le__exp_0) # label(axiom). [assumption].
% 1.09/1.52 40 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_Power_Opower__class_Opower(D,B,A)),c_Power_Opower__class_Opower(D,C,A))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Oone__class_Oone(A)),D)) # label(cls_power__increasing__iff_0) # label(axiom). [assumption].
% 1.09/1.52 41 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(hAPP(c_lessequals(A),c_Power_Opower__class_Opower(B,C,A)),c_Power_Opower__class_Opower(B,D,A))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),C),D)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Oone__class_Oone(A)),B)) # label(cls_power__increasing__iff_1) # label(axiom). [assumption].
% 1.09/1.52 42 -class_Ring__and__Field_Oordered__semidom(A) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Oone__class_Oone(A)),c_HOL_Ozero__class_Ozero(A))) # label(cls_not__one__le__zero_0) # label(axiom). [assumption].
% 1.09/1.52 43 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Oone__class_Oone(A)),c_Power_Opower__class_Opower(B,c_Suc(C),A))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Oone__class_Oone(A)),B)) # label(cls_power__gt1_0) # label(axiom). [assumption].
% 1.09/1.52 44 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),c_HOL_Oone__class_Oone(A))) # label(cls_zero__less__one_0) # label(axiom). [assumption].
% 1.09/1.52 45 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Oone__class_Oone(A)))) # label(cls_less__add__one_0) # label(axiom). [assumption].
% 1.09/1.52 46 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_Power_Opower__class_Opower(B,c_Suc(D),A)),c_Power_Opower__class_Opower(C,c_Suc(D),A))) # label(cls_power__le__imp__le__base_0) # label(axiom). [assumption].
% 1.09/1.52 47 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),c_Nat_Osemiring__1__class_Oof__nat(B,A))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),B)) # label(cls_of__nat__0__less__iff_1) # label(axiom). [assumption].
% 1.09/1.52 48 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),B)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),c_Nat_Osemiring__1__class_Oof__nat(B,A))) # label(cls_of__nat__0__less__iff_0) # label(axiom). [assumption].
% 1.09/1.52 49 -class_Ring__and__Field_Oordered__semidom(A) | c_Power_Opower__class_Opower(B,C,A) != c_Power_Opower__class_Opower(B,D,A) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Oone__class_Oone(A)),B)) | C = D # label(cls_power__inject__exp_0) # label(axiom). [assumption].
% 1.09/1.52 50 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),B),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_Power_Opower__class_Opower(D,B,A)),c_Power_Opower__class_Opower(D,C,A))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Oone__class_Oone(A)),D)) # label(cls_power__less__imp__less__exp_0) # label(axiom). [assumption].
% 1.09/1.52 51 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_Power_Opower__class_Opower(B,C,A)),c_Power_Opower__class_Opower(B,D,A))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Oone__class_Oone(A)),B)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),C),D)) # label(cls_power__strict__increasing_0) # label(axiom). [assumption].
% 1.09/1.52 52 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),B),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_Power_Opower__class_Opower(D,B,A)),c_Power_Opower__class_Opower(D,C,A))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Oone__class_Oone(A)),D)) # label(cls_power__strict__increasing__iff_0) # label(axiom). [assumption].
% 1.09/1.52 53 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_Power_Opower__class_Opower(B,C,A)),c_Power_Opower__class_Opower(B,D,A))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),C),D)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Oone__class_Oone(A)),B)) # label(cls_power__strict__increasing__iff_1) # label(axiom). [assumption].
% 1.09/1.52 54 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),D)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),C)) # label(cls_pos__add__strict_0) # label(axiom). [assumption].
% 1.09/1.52 55 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),B),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_Nat_Osemiring__1__class_Oof__nat(B,A)),c_Nat_Osemiring__1__class_Oof__nat(C,A))) # label(cls_of__nat__less__iff_0) # label(axiom). [assumption].
% 1.09/1.52 56 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_Nat_Osemiring__1__class_Oof__nat(B,A)),c_Nat_Osemiring__1__class_Oof__nat(C,A))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),B),C)) # label(cls_of__nat__less__iff_1) # label(axiom). [assumption].
% 1.09/1.52 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Power_Opower__class_Opower(A,c_Suc(B),tc_nat)),c_HOL_Oone__class_Oone(tc_nat))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A)). [resolve(17,a,18,a)].
% 1.09/1.52 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat)),c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)). [resolve(17,a,19,a)].
% 1.09/1.52 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat)),c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat))). [resolve(17,a,20,a)].
% 1.09/1.52 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Power_Opower__class_Opower(A,B,tc_nat))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A)). [resolve(17,a,21,a)].
% 1.09/1.52 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),c_Power_Opower__class_Opower(A,B,tc_nat))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),A)). [resolve(17,a,22,a)].
% 1.09/1.52 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Power_Opower__class_Opower(A,B,tc_nat)),c_Power_Opower__class_Opower(A,C,tc_nat))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),A)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),C)). [resolve(17,a,23,a)].
% 1.09/1.52 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Power_Opower__class_Opower(A,B,tc_nat)),c_Power_Opower__class_Opower(C,B,tc_nat))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),C)). [resolve(17,a,24,a)].
% 1.09/1.52 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),c_Power_Opower__class_Opower(A,B,tc_nat))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),B)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),A)). [resolve(17,a,25,a)].
% 1.09/1.52 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Power_Opower__class_Opower(A,B,tc_nat)),c_Power_Opower__class_Opower(C,B,tc_nat))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),C)). [resolve(17,a,26,a)].
% 1.09/1.52 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Power_Opower__class_Opower(A,B,tc_nat)),c_Power_Opower__class_Opower(A,C,tc_nat))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),C),B)). [resolve(17,a,27,a)].
% 1.09/1.52 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Power_Opower__class_Opower(A,B,tc_nat)),c_Power_Opower__class_Opower(A,C,tc_nat))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),C),B)). [resolve(17,a,28,a)].
% 1.09/1.52 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),B)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Power_Opower__class_Opower(A,C,tc_nat)),c_Power_Opower__class_Opower(B,C,tc_nat))). [resolve(17,a,29,a)].
% 1.09/1.52 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Power_Opower__class_Opower(A,B,tc_nat))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A)). [resolve(17,a,30,a)].
% 1.09/1.52 Derived: -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat))). [resolve(17,a,31,a)].
% 1.09/1.52 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat))). [resolve(17,a,32,a)].
% 1.09/1.52 Derived: -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat))). [resolve(17,a,33,a)].
% 1.09/1.52 Derived: c_Power_Opower__class_Opower(A,B,tc_nat) != c_Power_Opower__class_Opower(C,B,tc_nat) | A = C | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),C)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A)). [resolve(17,a,34,a)].
% 1.09/1.52 Derived: c_Power_Opower__class_Opower(A,c_Suc(B),tc_nat) != c_Power_Opower__class_Opower(C,c_Suc(B),tc_nat) | A = C | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),C)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A)). [resolve(17,a,35,a)].
% 1.09/1.52 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)))). [resolve(17,a,36,a)].
% 1.09/1.52 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat))). [resolve(17,a,37,a)].
% 1.09/1.52 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Power_Opower__class_Opower(C,A,tc_nat)),c_Power_Opower__class_Opower(C,B,tc_nat))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),C)). [resolve(17,a,39,a)].
% 1.09/1.52 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Power_Opower__class_Opower(A,B,tc_nat)),c_Power_Opower__class_Opower(A,C,tc_nat))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),A)). [resolve(17,a,41,a)].
% 1.09/1.52 Derived: -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat))). [resolve(17,a,42,a)].
% 1.09/1.52 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),c_Power_Opower__class_Opower(A,c_Suc(B),tc_nat))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),A)). [resolve(17,a,43,a)].
% 1.09/1.52 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat))). [resolve(17,a,44,a)].
% 1.09/1.52 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat)))). [resolve(17,a,45,a)].
% 1.09/1.52 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Power_Opower__class_Opower(A,c_Suc(C),tc_nat)),c_Power_Opower__class_Opower(B,c_Suc(C),tc_nat))). [resolve(17,a,46,a)].
% 1.09/1.52 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A)). [resolve(17,a,47,a)].
% 1.09/1.52 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat))). [resolve(17,a,48,a)].
% 1.09/1.52 Derived: c_Power_Opower__class_Opower(A,B,tc_nat) != c_Power_Opower__class_Opower(A,C,tc_nat) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),A)) | B = C. [resolve(17,a,49,a)].
% 1.09/1.54 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Power_Opower__class_Opower(C,A,tc_nat)),c_Power_Opower__class_Opower(C,B,tc_nat))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),C)). [resolve(17,a,50,a)].
% 1.09/1.54 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Power_Opower__class_Opower(A,B,tc_nat)),c_Power_Opower__class_Opower(A,C,tc_nat))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),A)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),B),C)). [resolve(17,a,51,a)].
% 1.09/1.54 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),B)). [resolve(17,a,54,a)].
% 1.09/1.54 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat)),c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat))). [resolve(17,a,55,a)].
% 1.09/1.54 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat)),c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B)). [resolve(17,a,56,a)].
% 1.09/1.54 57 class_OrderedGroup_Opordered__comm__monoid__add(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) # label(axiom). [assumption].
% 1.09/1.54 58 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C))) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),B)) # label(cls_add__nonneg__nonneg_0) # label(axiom). [assumption].
% 1.09/1.54 59 -class_OrderedGroup_Opordered__comm__monoid__add(A) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),c_HOL_Ozero__class_Ozero(A))) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),c_HOL_Ozero__class_Ozero(A)) = c_HOL_Ozero__class_Ozero(A) # label(cls_add__nonneg__eq__0__iff_2) # label(axiom). [assumption].
% 1.09/1.54 60 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),c_HOL_Ozero__class_Ozero(A))) # label(cls_add__neg__neg_0) # label(axiom). [assumption].
% 1.09/1.54 61 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),B)) # label(cls_add__nonneg__pos_0) # label(axiom). [assumption].
% 1.09/1.54 62 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C))) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),B)) # label(cls_add__pos__nonneg_0) # label(axiom). [assumption].
% 1.09/1.54 63 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) != c_HOL_Ozero__class_Ozero(A) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),B)) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_add__nonneg__eq__0__iff_1) # label(axiom). [assumption].
% 1.09/1.54 64 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) != c_HOL_Ozero__class_Ozero(A) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),B)) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_add__nonneg__eq__0__iff_0) # label(axiom). [assumption].
% 1.09/1.54 65 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),c_HOL_Ozero__class_Ozero(A))) # label(cls_add__nonpos__neg_0) # label(axiom). [assumption].
% 1.09/1.54 66 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(hAPP(c_lessequals(A),C),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),c_HOL_Ozero__class_Ozero(A))) # label(cls_add__neg__nonpos_0) # label(axiom). [assumption].
% 1.09/1.54 67 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),B)) # label(cls_add__pos__pos_0) # label(axiom). [assumption].
% 1.09/1.54 68 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hBOOL(hAPP(hAPP(c_lessequals(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(hAPP(c_lessequals(A),C),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),c_HOL_Ozero__class_Ozero(A))) # label(cls_add__nonpos__nonpos_0) # label(axiom). [assumption].
% 1.09/1.54 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A)). [resolve(57,a,58,a)].
% 1.09/1.54 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),B),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),c_HOL_Ozero__class_Ozero(tc_nat))). [resolve(57,a,60,a)].
% 1.09/1.54 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A)). [resolve(57,a,61,a)].
% 1.09/1.54 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),B)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A)). [resolve(57,a,62,a)].
% 1.09/1.54 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B) != c_HOL_Ozero__class_Ozero(tc_nat) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A)) | B = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(57,a,63,a)].
% 1.09/1.54 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B) != c_HOL_Ozero__class_Ozero(tc_nat) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A)) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(57,a,64,a)].
% 1.09/1.54 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),B),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),c_HOL_Ozero__class_Ozero(tc_nat))). [resolve(57,a,65,a)].
% 1.09/1.57 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),c_HOL_Ozero__class_Ozero(tc_nat))). [resolve(57,a,66,a)].
% 1.09/1.57 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),c_HOL_Ozero__class_Ozero(tc_nat))). [resolve(57,a,68,a)].
% 1.09/1.57 69 class_OrderedGroup_Ocomm__monoid__mult(tc_nat) # label(clsarity_nat__OrderedGroup_Ocomm__monoid__mult) # label(axiom). [assumption].
% 1.09/1.57 70 -class_OrderedGroup_Ocomm__monoid__mult(A) | c_Finite__Set_Osetprod(B,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C,A) = c_HOL_Oone__class_Oone(A) # label(cls_setprod__empty_0) # label(axiom). [assumption].
% 1.09/1.57 71 -class_OrderedGroup_Ocomm__monoid__mult(A) | c_Finite__Set_Osetprod(B,C,D,A) = c_HOL_Oone__class_Oone(A) | c_Finite__Set_Ofinite(C,D) # label(cls_setprod__def_1) # label(axiom). [assumption].
% 1.09/1.57 72 -class_OrderedGroup_Ocomm__monoid__mult(A) | c_Finite__Set_Osetprod(B,C,D,A) = c_HOL_Oone__class_Oone(A) | c_Finite__Set_Ofinite(C,D) # label(cls_setprod__infinite_0) # label(axiom). [assumption].
% 1.09/1.57 73 -class_OrderedGroup_Ocomm__monoid__mult(A) | c_Finite__Set_Osetprod(hAPP(c_COMBC(c_COMBS(hAPP(c_COMBB(c_HOL_OIf(A),tc_bool,tc_fun(A,tc_fun(A,A)),B),hAPP(c_COMBC(c_fequal(B),B,B,tc_bool),C)),D,B,A,tc_fun(A,A)),B,A,A),E),F,B,A) = c_Power_Opower__class_Opower(E,c_Finite__Set_Ocard(F,B),A) | hBOOL(hAPP(hAPP(c_in(B),C),F)) | -c_Finite__Set_Ofinite(F,B) # label(cls_setprod__gen__delta_1) # label(axiom). [assumption].
% 1.09/1.57 74 -class_OrderedGroup_Ocomm__monoid__mult(A) | c_Finite__Set_Osetprod(hAPP(c_COMBC(c_COMBS(hAPP(c_COMBB(c_HOL_OIf(A),tc_bool,tc_fun(A,tc_fun(A,A)),B),hAPP(c_fequal(B),C)),D,B,A,tc_fun(A,A)),B,A,A),c_HOL_Oone__class_Oone(A)),E,B,A) = hAPP(D,C) | -hBOOL(hAPP(hAPP(c_in(B),C),E)) | -c_Finite__Set_Ofinite(E,B) # label(cls_setprod__delta_H_0) # label(axiom). [assumption].
% 1.09/1.57 75 -class_OrderedGroup_Ocomm__monoid__mult(A) | c_Finite__Set_Osetprod(hAPP(c_COMBC(c_COMBS(hAPP(c_COMBB(c_HOL_OIf(A),tc_bool,tc_fun(A,tc_fun(A,A)),B),hAPP(c_fequal(B),C)),D,B,A,tc_fun(A,A)),B,A,A),c_HOL_Oone__class_Oone(A)),E,B,A) = c_HOL_Oone__class_Oone(A) | hBOOL(hAPP(hAPP(c_in(B),C),E)) | -c_Finite__Set_Ofinite(E,B) # label(cls_setprod__delta_H_1) # label(axiom). [assumption].
% 1.09/1.57 76 -class_OrderedGroup_Ocomm__monoid__mult(A) | c_Finite__Set_Osetprod(hAPP(c_COMBC(c_COMBS(hAPP(c_COMBB(c_HOL_OIf(A),tc_bool,tc_fun(A,tc_fun(A,A)),B),hAPP(c_COMBC(c_fequal(B),B,B,tc_bool),C)),D,B,A,tc_fun(A,A)),B,A,A),c_HOL_Oone__class_Oone(A)),E,B,A) = c_HOL_Oone__class_Oone(A) | hBOOL(hAPP(hAPP(c_in(B),C),E)) | -c_Finite__Set_Ofinite(E,B) # label(cls_setprod__delta_1) # label(axiom). [assumption].
% 1.09/1.57 77 -class_OrderedGroup_Ocomm__monoid__mult(A) | c_Finite__Set_Osetprod(hAPP(c_COMBC(c_COMBS(hAPP(c_COMBB(c_HOL_OIf(A),tc_bool,tc_fun(A,tc_fun(A,A)),B),hAPP(c_COMBC(c_fequal(B),B,B,tc_bool),C)),D,B,A,tc_fun(A,A)),B,A,A),c_HOL_Oone__class_Oone(A)),E,B,A) = hAPP(D,C) | -hBOOL(hAPP(hAPP(c_in(B),C),E)) | -c_Finite__Set_Ofinite(E,B) # label(cls_setprod__delta_0) # label(axiom). [assumption].
% 1.09/1.57 Derived: c_Finite__Set_Osetprod(A,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B,tc_nat) = c_HOL_Oone__class_Oone(tc_nat). [resolve(69,a,70,a)].
% 1.09/1.57 Derived: c_Finite__Set_Osetprod(A,B,C,tc_nat) = c_HOL_Oone__class_Oone(tc_nat) | c_Finite__Set_Ofinite(B,C). [resolve(69,a,71,a)].
% 1.09/1.57 Derived: c_Finite__Set_Osetprod(hAPP(c_COMBC(c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_nat),tc_bool,tc_fun(tc_nat,tc_fun(tc_nat,tc_nat)),A),hAPP(c_COMBC(c_fequal(A),A,A,tc_bool),B)),C,A,tc_nat,tc_fun(tc_nat,tc_nat)),A,tc_nat,tc_nat),D),E,A,tc_nat) = c_Power_Opower__class_Opower(D,c_Finite__Set_Ocard(E,A),tc_nat) | hBOOL(hAPP(hAPP(c_in(A),B),E)) | -c_Finite__Set_Ofinite(E,A). [resolve(69,a,73,a)].
% 1.09/1.65 Derived: c_Finite__Set_Osetprod(hAPP(c_COMBC(c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_nat),tc_bool,tc_fun(tc_nat,tc_fun(tc_nat,tc_nat)),A),hAPP(c_fequal(A),B)),C,A,tc_nat,tc_fun(tc_nat,tc_nat)),A,tc_nat,tc_nat),c_HOL_Oone__class_Oone(tc_nat)),D,A,tc_nat) = hAPP(C,B) | -hBOOL(hAPP(hAPP(c_in(A),B),D)) | -c_Finite__Set_Ofinite(D,A). [resolve(69,a,74,a)].
% 1.09/1.65 Derived: c_Finite__Set_Osetprod(hAPP(c_COMBC(c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_nat),tc_bool,tc_fun(tc_nat,tc_fun(tc_nat,tc_nat)),A),hAPP(c_fequal(A),B)),C,A,tc_nat,tc_fun(tc_nat,tc_nat)),A,tc_nat,tc_nat),c_HOL_Oone__class_Oone(tc_nat)),D,A,tc_nat) = c_HOL_Oone__class_Oone(tc_nat) | hBOOL(hAPP(hAPP(c_in(A),B),D)) | -c_Finite__Set_Ofinite(D,A). [resolve(69,a,75,a)].
% 1.09/1.65 Derived: c_Finite__Set_Osetprod(hAPP(c_COMBC(c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_nat),tc_bool,tc_fun(tc_nat,tc_fun(tc_nat,tc_nat)),A),hAPP(c_COMBC(c_fequal(A),A,A,tc_bool),B)),C,A,tc_nat,tc_fun(tc_nat,tc_nat)),A,tc_nat,tc_nat),c_HOL_Oone__class_Oone(tc_nat)),D,A,tc_nat) = c_HOL_Oone__class_Oone(tc_nat) | hBOOL(hAPP(hAPP(c_in(A),B),D)) | -c_Finite__Set_Ofinite(D,A). [resolve(69,a,76,a)].
% 1.09/1.65 Derived: c_Finite__Set_Osetprod(hAPP(c_COMBC(c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_nat),tc_bool,tc_fun(tc_nat,tc_fun(tc_nat,tc_nat)),A),hAPP(c_COMBC(c_fequal(A),A,A,tc_bool),B)),C,A,tc_nat,tc_fun(tc_nat,tc_nat)),A,tc_nat,tc_nat),c_HOL_Oone__class_Oone(tc_nat)),D,A,tc_nat) = hAPP(C,B) | -hBOOL(hAPP(hAPP(c_in(A),B),D)) | -c_Finite__Set_Ofinite(D,A). [resolve(69,a,77,a)].
% 1.09/1.65 78 class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add) # label(axiom). [assumption].
% 1.09/1.65 79 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | hBOOL(hAPP(hAPP(c_lessequals(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),E))) | -hBOOL(hAPP(hAPP(c_lessequals(A),C),E)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),D)) # label(cls_add__mono_0) # label(axiom). [assumption].
% 1.09/1.65 80 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | hBOOL(hAPP(hAPP(c_lessequals(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C))) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),D)) # label(cls_add__right__mono_0) # label(axiom). [assumption].
% 1.09/1.65 81 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | hBOOL(hAPP(hAPP(c_lessequals(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D))) | -hBOOL(hAPP(hAPP(c_lessequals(A),C),D)) # label(cls_add__left__mono_0) # label(axiom). [assumption].
% 1.09/1.65 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),D)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),C)). [resolve(78,a,79,a)].
% 1.09/1.65 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),C)). [resolve(78,a,80,a)].
% 1.09/1.65 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),C)). [resolve(78,a,81,a)].
% 1.09/1.65 82 class_Ring__and__Field_Osemiring__0(tc_nat) # label(clsarity_nat__Ring__and__Field_Osemiring__0) # label(axiom). [assumption].
% 1.09/1.65 83 -class_Ring__and__Field_Osemiring__0(A) | -class_Power_Opower(A) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(tc_nat),A) = c_HOL_Oone__class_Oone(A) # label(cls_power__0__left_0) # label(axiom). [assumption].
% 1.09/1.65 84 -class_Ring__and__Field_Osemiring__0(A) | -class_Power_Opower(A) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),c_Suc(B),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_power__0__Suc_0) # label(axiom). [assumption].
% 1.09/1.65 85 -class_Ring__and__Field_Osemiring__0(A) | -class_Power_Opower(A) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),B,A) = c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(tc_nat) # label(cls_power__0__left_1) # label(axiom). [assumption].
% 1.43/1.69 Derived: -class_Power_Opower(tc_nat) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(A),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(82,a,84,a)].
% 1.43/1.69 Derived: -class_Power_Opower(tc_nat) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(82,a,85,a)].
% 1.43/1.69 86 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) # label(axiom). [assumption].
% 1.43/1.69 87 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_OrderedGroup_Ocomm__monoid__add(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D))) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),D)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),C)) # label(cls_add__strict__increasing_0) # label(axiom). [assumption].
% 1.43/1.69 88 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_OrderedGroup_Ocomm__monoid__add(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),D)) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),C)) # label(cls_add__strict__increasing2_0) # label(axiom). [assumption].
% 1.43/1.69 89 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_OrderedGroup_Ocomm__monoid__add(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D))) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),D)) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),C)) # label(cls_add__increasing_0) # label(axiom). [assumption].
% 1.43/1.69 90 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_OrderedGroup_Ocomm__monoid__add(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D))) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),D)) # label(cls_add__increasing2_0) # label(axiom). [assumption].
% 1.43/1.69 91 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | hBOOL(hAPP(hAPP(c_lessequals(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C))) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),D)) # label(cls_add__le__cancel__right_1) # label(axiom). [assumption].
% 1.43/1.69 92 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D))) # label(cls_add__le__cancel__right_0) # label(axiom). [assumption].
% 1.43/1.69 93 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | hBOOL(hAPP(hAPP(c_lessequals(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D))) | -hBOOL(hAPP(hAPP(c_lessequals(A),C),D)) # label(cls_add__le__cancel__left_1) # label(axiom). [assumption].
% 1.43/1.69 94 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C))) # label(cls_add__le__cancel__left_0) # label(axiom). [assumption].
% 1.43/1.69 95 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C))) # label(cls_add__less__cancel__left_0) # label(axiom). [assumption].
% 1.43/1.69 96 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),D)) # label(cls_add__less__cancel__left_1) # label(axiom). [assumption].
% 1.43/1.69 97 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D))) # label(cls_add__less__cancel__right_0) # label(axiom). [assumption].
% 1.43/1.74 98 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),D)) # label(cls_add__less__cancel__right_1) # label(axiom). [assumption].
% 1.43/1.74 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_nat) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),B)). [resolve(86,a,87,a)].
% 1.43/1.74 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_nat) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),C)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),B)). [resolve(86,a,88,a)].
% 1.43/1.74 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_nat) | hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),C)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),B)). [resolve(86,a,89,a)].
% 1.43/1.74 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_nat) | hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),C)). [resolve(86,a,90,a)].
% 1.43/1.74 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C))). [resolve(86,a,92,a)].
% 1.43/1.74 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),A)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B))). [resolve(86,a,94,a)].
% 1.43/1.74 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),A)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B))). [resolve(86,a,95,a)].
% 1.43/1.74 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),B),C)). [resolve(86,a,96,a)].
% 1.43/1.74 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C))). [resolve(86,a,97,a)].
% 1.43/1.74 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),C)). [resolve(86,a,98,a)].
% 1.43/1.74 99 class_OrderedGroup_Oab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Oab__semigroup__add) # label(axiom). [assumption].
% 1.43/1.74 100 -class_OrderedGroup_Oab__semigroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) # label(cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) # label(axiom). [assumption].
% 1.43/1.74 101 class_Ring__and__Field_Ozero__neq__one(tc_nat) # label(clsarity_nat__Ring__and__Field_Ozero__neq__one) # label(axiom). [assumption].
% 1.43/1.74 102 -class_Ring__and__Field_Ozero__neq__one(A) | -class_Ring__and__Field_Ono__zero__divisors(A) | -class_Ring__and__Field_Omult__zero(A) | -class_Power_Opower(A) | c_Power_Opower__class_Opower(B,c_HOL_Ozero__class_Ozero(tc_nat),A) != c_HOL_Ozero__class_Ozero(A) # label(cls_power__eq__0__iff_1) # label(axiom). [assumption].
% 1.43/1.74 103 -class_Ring__and__Field_Ozero__neq__one(A) | c_HOL_Ozero__class_Ozero(A) != c_HOL_Oone__class_Oone(A) # label(cls_zero__neq__one_0) # label(axiom). [assumption].
% 1.53/1.79 104 -class_Ring__and__Field_Ozero__neq__one(A) | c_HOL_Oone__class_Oone(A) != c_HOL_Ozero__class_Ozero(A) # label(cls_one__neq__zero_0) # label(axiom). [assumption].
% 1.53/1.79 105 -class_Ring__and__Field_Ozero__neq__one(A) | -class_Ring__and__Field_Ono__zero__divisors(A) | -class_Ring__and__Field_Omult__zero(A) | -class_Power_Opower(A) | c_Power_Opower__class_Opower(B,C,A) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_power__eq__0__iff_0) # label(axiom). [assumption].
% 1.53/1.79 106 -class_Ring__and__Field_Ozero__neq__one(A) | -class_Ring__and__Field_Ono__zero__divisors(A) | -class_Ring__and__Field_Omult__zero(A) | -class_Power_Opower(A) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),B,A) = c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(tc_nat) # label(cls_power__eq__0__iff_2) # label(axiom). [assumption].
% 1.53/1.79 Derived: -class_Ring__and__Field_Ono__zero__divisors(tc_nat) | -class_Ring__and__Field_Omult__zero(tc_nat) | -class_Power_Opower(tc_nat) | c_Power_Opower__class_Opower(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat). [resolve(101,a,102,a)].
% 1.53/1.79 Derived: c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oone__class_Oone(tc_nat). [resolve(101,a,103,a)].
% 1.53/1.79 Derived: c_HOL_Oone__class_Oone(tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat). [resolve(101,a,104,a)].
% 1.53/1.79 Derived: -class_Ring__and__Field_Ono__zero__divisors(tc_nat) | -class_Ring__and__Field_Omult__zero(tc_nat) | -class_Power_Opower(tc_nat) | c_Power_Opower__class_Opower(A,B,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(101,a,105,a)].
% 1.53/1.79 107 class_OrderedGroup_Omonoid__mult(tc_nat) # label(clsarity_nat__OrderedGroup_Omonoid__mult) # label(axiom). [assumption].
% 1.53/1.79 108 -class_OrderedGroup_Omonoid__mult(A) | c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(A),B,A) = c_HOL_Oone__class_Oone(A) # label(cls_power__one_0) # label(axiom). [assumption].
% 1.53/1.79 109 -class_OrderedGroup_Omonoid__mult(A) | c_Power_Opower__class_Opower(B,c_HOL_Oone__class_Oone(tc_nat),A) = B # label(cls_power__one__right_0) # label(axiom). [assumption].
% 1.53/1.79 Derived: c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat) = c_HOL_Oone__class_Oone(tc_nat). [resolve(107,a,108,a)].
% 1.53/1.79 110 class_Ring__and__Field_Osemiring__1(tc_nat) # label(clsarity_nat__Ring__and__Field_Osemiring__1) # label(axiom). [assumption].
% 1.53/1.79 111 -class_Ring__and__Field_Osemiring__1(A) | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),A) = c_HOL_Oone__class_Oone(A) # label(cls_of__nat__1_0) # label(axiom). [assumption].
% 1.53/1.79 112 -class_Ring__and__Field_Osemiring__1(A) | c_Nat_Osemiring__1__class_Oof__nat(c_Suc(B),A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Oone__class_Oone(A)),c_Nat_Osemiring__1__class_Oof__nat(B,A)) # label(cls_of__nat__Suc_0) # label(axiom). [assumption].
% 1.53/1.79 113 -class_Ring__and__Field_Osemiring__1(A) | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_of__nat__0_0) # label(axiom). [assumption].
% 1.53/1.79 114 -class_Ring__and__Field_Osemiring__1(A) | c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Nat_Osemiring__1__class_Oof__nat(B,A)),c_Nat_Osemiring__1__class_Oof__nat(C,A)) # label(cls_of__nat__add_0) # label(axiom). [assumption].
% 1.53/1.79 Derived: c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_HOL_Oone__class_Oone(tc_nat). [resolve(110,a,111,a)].
% 1.53/1.79 Derived: c_Nat_Osemiring__1__class_Oof__nat(c_Suc(A),tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat)). [resolve(110,a,112,a)].
% 1.53/1.79 Derived: c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(110,a,113,a)].
% 1.53/1.79 Derived: c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat)),c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat)). [resolve(110,a,114,a)].
% 1.57/1.81 115 class_Lattices_Olower__semilattice(tc_fun(A,B)) | -class_Lattices_Olattice(B) # label(clsarity_fun__Lattices_Olower__semilattice) # label(axiom). [assumption].
% 1.57/1.81 116 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,A) = B | -hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) # label(cls_le__iff__inf_0) # label(axiom). [assumption].
% 1.57/1.81 117 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,A) != B | hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) # label(cls_le__iff__inf_1) # label(axiom). [assumption].
% 1.57/1.81 118 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,A) = C | -hBOOL(hAPP(hAPP(c_lessequals(A),C),B)) # label(cls_inf__absorb2_0) # label(axiom). [assumption].
% 1.57/1.81 119 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,A) = c_Lattices_Olower__semilattice__class_Oinf(C,B,A) # label(cls_inf__commute_0) # label(axiom). [assumption].
% 1.57/1.81 120 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,A),A) = c_Lattices_Olower__semilattice__class_Oinf(C,c_Lattices_Olower__semilattice__class_Oinf(B,D,A),A) # label(cls_inf__left__commute_0) # label(axiom). [assumption].
% 1.57/1.81 121 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(B,C,A),D,A) = c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,A),A) # label(cls_inf__assoc_0) # label(axiom). [assumption].
% 1.57/1.81 122 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),c_Lattices_Olower__semilattice__class_Oinf(C,D,A))) # label(cls_le__infE_0) # label(axiom). [assumption].
% 1.57/1.81 123 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),c_Lattices_Olower__semilattice__class_Oinf(D,C,A))) # label(cls_le__infE_1) # label(axiom). [assumption].
% 1.57/1.81 124 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),c_Lattices_Olower__semilattice__class_Oinf(B,C,A)),D)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),D)) # label(cls_le__infI1_0) # label(axiom). [assumption].
% 1.57/1.81 125 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),c_Lattices_Olower__semilattice__class_Oinf(B,C,A)),D)) | -hBOOL(hAPP(hAPP(c_lessequals(A),C),D)) # label(cls_le__infI2_0) # label(axiom). [assumption].
% 1.57/1.81 126 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),c_Lattices_Olower__semilattice__class_Oinf(C,D,A))) # label(cls_le__inf__iff_0) # label(axiom). [assumption].
% 1.57/1.81 127 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),c_Lattices_Olower__semilattice__class_Oinf(D,C,A))) # label(cls_le__inf__iff_1) # label(axiom). [assumption].
% 1.57/1.81 128 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_Lattices_Olower__semilattice__class_Oinf(B,C,A)),D)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),D)) # label(cls_less__infI1_0) # label(axiom). [assumption].
% 1.57/1.81 129 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_Lattices_Olower__semilattice__class_Oinf(B,C,A)),D)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),D)) # label(cls_less__infI2_0) # label(axiom). [assumption].
% 1.57/1.81 130 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),c_Lattices_Olower__semilattice__class_Oinf(C,D,A))) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),D)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) # label(cls_inf__greatest_0) # label(axiom). [assumption].
% 1.57/1.81 131 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),c_Lattices_Olower__semilattice__class_Oinf(C,D,A))) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),D)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) # label(cls_le__inf__iff_2) # label(axiom). [assumption].
% 1.57/1.81 132 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),c_Lattices_Olower__semilattice__class_Oinf(C,D,A))) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),D)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) # label(cls_le__infI_0) # label(axiom). [assumption].
% 1.57/1.81 133 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),c_Lattices_Olower__semilattice__class_Oinf(B,C,A)),C)) # label(cls_inf__le2_0) # label(axiom). [assumption].
% 1.57/1.81 134 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),c_Lattices_Olower__semilattice__class_Oinf(B,C,A)),B)) # label(cls_inf__le1_0) # label(axiom). [assumption].
% 1.57/1.81 135 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(B,C,A),A) = c_Lattices_Olower__semilattice__class_Oinf(B,C,A) # label(cls_inf__left__idem_0) # label(axiom). [assumption].
% 1.57/1.81 136 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,B,A) = B # label(cls_inf__idem_0) # label(axiom). [assumption].
% 1.57/1.81 Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)) = B | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(D,A)),B),C)). [resolve(115,a,116,a)].
% 1.57/1.81 Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)) != B | hBOOL(hAPP(hAPP(c_lessequals(tc_fun(D,A)),B),C)). [resolve(115,a,117,a)].
% 1.57/1.81 Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)) = C | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(D,A)),C),B)). [resolve(115,a,118,a)].
% 1.57/1.81 Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)) = c_Lattices_Olower__semilattice__class_Oinf(C,B,tc_fun(D,A)). [resolve(115,a,119,a)].
% 1.57/1.81 Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,tc_fun(E,A)),tc_fun(E,A)) = c_Lattices_Olower__semilattice__class_Oinf(C,c_Lattices_Olower__semilattice__class_Oinf(B,D,tc_fun(E,A)),tc_fun(E,A)). [resolve(115,a,120,a)].
% 1.57/1.81 Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)),E,tc_fun(D,A)) = c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(C,E,tc_fun(D,A)),tc_fun(D,A)). [resolve(115,a,121,a)].
% 1.57/1.81 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),C),D)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),C),c_Lattices_Olower__semilattice__class_Oinf(D,E,tc_fun(B,A)))). [resolve(115,a,122,a)].
% 1.57/1.81 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),C),D)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),C),c_Lattices_Olower__semilattice__class_Oinf(E,D,tc_fun(B,A)))). [resolve(115,a,123,a)].
% 1.57/1.81 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),c_Lattices_Olower__semilattice__class_Oinf(C,D,tc_fun(B,A))),E)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),C),E)). [resolve(115,a,124,a)].
% 1.57/1.81 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),c_Lattices_Olower__semilattice__class_Oinf(C,D,tc_fun(B,A))),E)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),D),E)). [resolve(115,a,125,a)].
% 1.57/1.81 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(B,A)),c_Lattices_Olower__semilattice__class_Oinf(C,D,tc_fun(B,A))),E)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(B,A)),C),E)). [resolve(115,a,128,a)].
% 1.57/1.81 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(B,A)),c_Lattices_Olower__semilattice__class_Oinf(C,D,tc_fun(B,A))),E)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(B,A)),D),E)). [resolve(115,a,129,a)].
% 1.57/1.81 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),C),c_Lattices_Olower__semilattice__class_Oinf(D,E,tc_fun(B,A)))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),C),E)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),C),D)). [resolve(115,a,130,a)].
% 1.57/1.81 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),c_Lattices_Olower__semilattice__class_Oinf(C,D,tc_fun(B,A))),D)). [resolve(115,a,133,a)].
% 1.57/1.81 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),c_Lattices_Olower__semilattice__class_Oinf(C,D,tc_fun(B,A))),C)). [resolve(115,a,134,a)].
% 1.57/1.81 Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)),tc_fun(D,A)) = c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)). [resolve(115,a,135,a)].
% 1.57/1.81 Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,B,tc_fun(C,A)) = B. [resolve(115,a,136,a)].
% 1.57/1.81 137 class_Lattices_Olower__semilattice(tc_nat) # label(clsarity_nat__Lattices_Olower__semilattice) # label(axiom). [assumption].
% 1.57/1.81 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat) = A | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)). [resolve(137,a,116,a)].
% 1.57/1.81 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat) != A | hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)). [resolve(137,a,117,a)].
% 1.57/1.81 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat) = B | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),A)). [resolve(137,a,118,a)].
% 1.57/1.81 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(B,A,tc_nat). [resolve(137,a,119,a)].
% 1.57/1.81 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_nat),tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(A,C,tc_nat),tc_nat). [resolve(137,a,120,a)].
% 1.57/1.81 Derived: c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat),C,tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_nat),tc_nat). [resolve(137,a,121,a)].
% 1.57/1.81 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_nat))). [resolve(137,a,122,a)].
% 1.57/1.81 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),c_Lattices_Olower__semilattice__class_Oinf(C,B,tc_nat))). [resolve(137,a,123,a)].
% 1.57/1.81 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat)),C)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),C)). [resolve(137,a,124,a)].
% 1.57/1.81 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat)),C)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),C)). [resolve(137,a,125,a)].
% 1.57/1.81 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat)),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),C)). [resolve(137,a,128,a)].
% 1.57/1.81 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat)),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),B),C)). [resolve(137,a,129,a)].
% 1.57/1.81 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_nat))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),C)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)). [resolve(137,a,130,a)].
% 1.57/1.81 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat)),B)). [resolve(137,a,133,a)].
% 1.57/1.81 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat)),A)). [resolve(137,a,134,a)].
% 1.57/1.81 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat),tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat). [resolve(137,a,135,a)].
% 1.57/1.81 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,A,tc_nat) = A. [resolve(137,a,136,a)].
% 1.57/1.81 138 class_Lattices_Olower__semilattice(tc_bool) # label(clsarity_bool__Lattices_Olower__semilattice) # label(axiom). [assumption].
% 1.57/1.81 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool) = A | -hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),B)). [resolve(138,a,116,a)].
% 1.57/1.83 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool) != A | hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),B)). [resolve(138,a,117,a)].
% 1.57/1.83 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool) = B | -hBOOL(hAPP(hAPP(c_lessequals(tc_bool),B),A)). [resolve(138,a,118,a)].
% 1.57/1.83 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(B,A,tc_bool). [resolve(138,a,119,a)].
% 1.57/1.83 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_bool),tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(A,C,tc_bool),tc_bool). [resolve(138,a,120,a)].
% 1.57/1.83 Derived: c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),C,tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_bool),tc_bool). [resolve(138,a,121,a)].
% 1.57/1.83 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_bool))). [resolve(138,a,122,a)].
% 1.57/1.83 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),c_Lattices_Olower__semilattice__class_Oinf(C,B,tc_bool))). [resolve(138,a,123,a)].
% 1.57/1.83 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_bool),c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool)),C)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),C)). [resolve(138,a,124,a)].
% 1.57/1.83 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_bool),c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool)),C)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_bool),B),C)). [resolve(138,a,125,a)].
% 1.57/1.83 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_bool),c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool)),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_bool),A),C)). [resolve(138,a,128,a)].
% 1.57/1.83 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_bool),c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool)),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_bool),B),C)). [resolve(138,a,129,a)].
% 1.57/1.83 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_bool))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),C)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),B)). [resolve(138,a,130,a)].
% 1.57/1.83 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_bool),c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool)),B)). [resolve(138,a,133,a)].
% 1.57/1.83 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_bool),c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool)),A)). [resolve(138,a,134,a)].
% 1.57/1.83 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool). [resolve(138,a,135,a)].
% 1.57/1.83 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,A,tc_bool) = A. [resolve(138,a,136,a)].
% 1.57/1.83 139 class_Orderings_Olinorder(tc_nat) # label(clsarity_nat__Orderings_Olinorder) # label(axiom). [assumption].
% 1.57/1.83 140 -class_Orderings_Olinorder(A) | c_SetInterval_Oord__class_OlessThan(B,A) != c_SetInterval_Oord__class_OlessThan(C,A) | B = C # label(cls_lessThan__eq__iff_0) # label(axiom). [assumption].
% 1.57/1.83 141 -class_Orderings_Olinorder(A) | c_SetInterval_Oord__class_OgreaterThan(B,A) != c_SetInterval_Oord__class_OgreaterThan(C,A) | B = C # label(cls_greaterThan__eq__iff_0) # label(axiom). [assumption].
% 1.57/1.83 142 -class_Orderings_Olinorder(A) | B = C | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) # label(cls_linorder__antisym__conv2_0) # label(axiom). [assumption].
% 1.57/1.83 143 -class_Orderings_Olinorder(A) | B = C | -hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) # label(cls_linorder__antisym__conv1_0) # label(axiom). [assumption].
% 1.57/1.83 144 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) | hBOOL(hAPP(hAPP(c_lessequals(A),C),B)) # label(cls_not__leE_0) # label(axiom). [assumption].
% 1.57/1.83 145 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),B)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),B)) # label(cls_linorder__antisym__conv2_1) # label(axiom). [assumption].
% 1.57/1.83 146 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),B)) | hBOOL(hAPP(hAPP(c_lessequals(A),B),B)) # label(cls_linorder__antisym__conv1_1) # label(axiom). [assumption].
% 1.57/1.83 147 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),C),B)) # label(cls_linorder__not__less_1) # label(axiom). [assumption].
% 1.57/1.83 148 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),B)) # label(cls_linorder__not__less_0) # label(axiom). [assumption].
% 1.57/1.83 149 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),B)) # label(cls_linorder__not__le_1) # label(axiom). [assumption].
% 1.57/1.83 150 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) | hBOOL(hAPP(hAPP(c_lessequals(A),C),B)) # label(cls_linorder__not__le_0) # label(axiom). [assumption].
% 1.57/1.83 151 -class_Orderings_Olinorder(A) | c_Orderings_Olinorder(c_COMBC(c_lessequals(A),A,A,tc_bool),c_COMBC(c_HOL_Oord__class_Oless(A),A,A,tc_bool),A) # label(cls_dual__linorder_0) # label(axiom). [assumption].
% 1.57/1.83 152 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) | hBOOL(hAPP(hAPP(c_lessequals(A),C),B)) # label(cls_linorder__linear_0) # label(axiom). [assumption].
% 1.57/1.83 153 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),B)) # label(cls_not__less__iff__gr__or__eq_1) # label(axiom). [assumption].
% 1.57/1.83 154 -class_Orderings_Olinorder(A) | B = C | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),B)) # label(cls_linorder__antisym__conv3_0) # label(axiom). [assumption].
% 1.57/1.83 155 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) | C = B | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),B)) # label(cls_linorder__less__linear_0) # label(axiom). [assumption].
% 1.57/1.83 156 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),B)) | C = B # label(cls_linorder__neqE_0) # label(axiom). [assumption].
% 1.57/1.83 157 -class_Orderings_Olinorder(A) | B = C | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),B)) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) # label(cls_not__less__iff__gr__or__eq_0) # label(axiom). [assumption].
% 1.57/1.83 158 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),B)) # label(cls_linorder__neq__iff_1) # label(axiom). [assumption].
% 1.57/1.83 Derived: c_SetInterval_Oord__class_OlessThan(A,tc_nat) != c_SetInterval_Oord__class_OlessThan(B,tc_nat) | A = B. [resolve(139,a,140,a)].
% 1.57/1.83 Derived: c_SetInterval_Oord__class_OgreaterThan(A,tc_nat) != c_SetInterval_Oord__class_OgreaterThan(B,tc_nat) | A = B. [resolve(139,a,141,a)].
% 1.57/1.83 Derived: A = B | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)). [resolve(139,a,142,a)].
% 1.57/1.83 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B)) | hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),A)). [resolve(139,a,144,a)].
% 1.57/1.83 Derived: -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),A)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),A)). [resolve(139,a,145,a)].
% 1.57/1.83 Derived: -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),A)). [resolve(139,a,147,a)].
% 1.57/1.83 Derived: c_Orderings_Olinorder(c_COMBC(c_lessequals(tc_nat),tc_nat,tc_nat,tc_bool),c_COMBC(c_HOL_Oord__class_Oless(tc_nat),tc_nat,tc_nat,tc_bool),tc_nat). [resolve(139,a,151,a)].
% 1.57/1.83 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)) | hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),A)). [resolve(139,a,152,a)].
% 1.57/1.83 Derived: -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),B),A)). [resolve(139,a,153,a)].
% 1.57/1.83 Derived: A = B | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B)) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),B),A)). [resolve(139,a,154,a)].
% 1.68/1.93 159 hAPP(A,B) = hAPP(B,C) | -hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),B),c_Arrow__Order__Mirabelle_OProf)) | -c_Arrow__Order__Mirabelle_Odictator(A,C) # label(cls_dictator__def_0) # label(axiom). [assumption].
% 1.68/1.93 160 hAPP(A,v_sko__Arrow__Order__Mirabelle__Xdictator__def__1(A,B)) != hAPP(v_sko__Arrow__Order__Mirabelle__Xdictator__def__1(A,B),B) | c_Arrow__Order__Mirabelle_Odictator(A,B) # label(cls_dictator__def_2) # label(axiom). [assumption].
% 1.68/1.93 161 c_Arrow__Order__Mirabelle_Odictator(A,B) | hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_sko__Arrow__Order__Mirabelle__Xdictator__def__1(A,B)),c_Arrow__Order__Mirabelle_OProf)) # label(cls_dictator__def_1) # label(axiom). [assumption].
% 1.68/1.93 Derived: hAPP(A,B) = hAPP(B,C) | -hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),B),c_Arrow__Order__Mirabelle_OProf)) | hAPP(A,v_sko__Arrow__Order__Mirabelle__Xdictator__def__1(A,C)) != hAPP(v_sko__Arrow__Order__Mirabelle__Xdictator__def__1(A,C),C). [resolve(159,c,160,b)].
% 1.68/1.93 Derived: hAPP(A,B) = hAPP(B,C) | -hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),B),c_Arrow__Order__Mirabelle_OProf)) | hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_sko__Arrow__Order__Mirabelle__Xdictator__def__1(A,C)),c_Arrow__Order__Mirabelle_OProf)). [resolve(159,c,161,a)].
% 1.68/1.93 162 class_OrderedGroup_Osemigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Osemigroup__add) # label(axiom). [assumption].
% 1.68/1.93 163 -class_OrderedGroup_Osemigroup__add(A) | c_List_Ofoldl(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),D,A,A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(A),C,D,A,A)) # label(cls_foldl__assoc_0) # label(axiom). [assumption].
% 1.68/1.93 Derived: c_List_Ofoldl(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),C,tc_nat,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(tc_nat),B,C,tc_nat,tc_nat)). [resolve(162,a,163,a)].
% 1.68/1.93 164 class_Nat_Osemiring__char__0(tc_nat) # label(clsarity_nat__Nat_Osemiring__char__0) # label(axiom). [assumption].
% 1.68/1.93 165 -class_Nat_Osemiring__char__0(A) | c_Nat_Osemiring__1__class_Oof__nat(B,A) != c_Nat_Osemiring__1__class_Oof__nat(C,A) | B = C # label(cls_of__nat__eq__iff_0) # label(axiom). [assumption].
% 1.68/1.93 Derived: c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat) != c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat) | A = B. [resolve(164,a,165,a)].
% 1.68/1.93 166 class_OrderedGroup_Omonoid__add(tc_nat) # label(clsarity_nat__OrderedGroup_Omonoid__add) # label(axiom). [assumption].
% 1.68/1.93 167 -class_OrderedGroup_Omonoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A),C,A,A)) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(A),B,C,A,A) # label(cls_foldl__absorb0_0) # label(axiom). [assumption].
% 1.68/1.93 168 -class_OrderedGroup_Omonoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),B) = B # label(cls_add__0__left_0) # label(axiom). [assumption].
% 1.68/1.93 169 -class_OrderedGroup_Omonoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Ozero__class_Ozero(A)) = B # label(cls_monoid__add__class_Oadd__0__right_0) # label(axiom). [assumption].
% 1.68/1.93 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat,tc_nat)) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(tc_nat),A,B,tc_nat,tc_nat). [resolve(166,a,167,a)].
% 1.68/1.93 170 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 1.74/2.05 171 -class_OrderedGroup_Ocancel__ab__semigroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D) | C = D # label(cls_add__imp__eq_0) # label(axiom). [assumption].
% 1.74/2.05 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C) | B = C. [resolve(170,a,171,a)].
% 1.74/2.05 172 class_OrderedGroup_Ocancel__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocancel__semigroup__add) # label(axiom). [assumption].
% 1.74/2.05 173 -class_OrderedGroup_Ocancel__semigroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D) | C = D # label(cls_add__left__cancel_0) # label(axiom). [assumption].
% 1.74/2.05 174 -class_OrderedGroup_Ocancel__semigroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C) | B = D # label(cls_add__right__cancel_0) # label(axiom). [assumption].
% 1.74/2.05 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B) | A = C. [resolve(172,a,174,a)].
% 1.74/2.05 175 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) # label(axiom). [assumption].
% 1.74/2.05 176 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),E))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),E)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),D)) # label(cls_add__le__less__mono_0) # label(axiom). [assumption].
% 1.74/2.05 177 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),E))) | -hBOOL(hAPP(hAPP(c_lessequals(A),C),E)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),D)) # label(cls_add__less__le__mono_0) # label(axiom). [assumption].
% 1.74/2.05 178 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),D)) # label(cls_add__strict__left__mono_0) # label(axiom). [assumption].
% 1.74/2.05 179 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),D)) # label(cls_add__strict__right__mono_0) # label(axiom). [assumption].
% 1.74/2.05 180 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),E))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),E)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),D)) # label(cls_add__strict__mono_0) # label(axiom). [assumption].
% 1.74/2.05 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),B),D)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),C)). [resolve(175,a,176,a)].
% 1.74/2.05 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),D)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),C)). [resolve(175,a,177,a)].
% 1.74/2.05 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),B),D)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),C)). [resolve(175,a,180,a)].
% 1.74/2.05
% 1.74/2.05 ============================== end predicate elimination =============
% 1.74/2.05
% 1.74/2.05 Auto_denials: (non-Horn, no changes).
% 1.74/2.05
% 1.74/2.05 Term ordering decisions:
% 1.74/2.05 Function symbol KB weights: tc_nat=1. tc_bool=1. tc_Arrow__Order__Mirabelle_Oalt=1. tc_Arrow__Order__Mirabelle_Oindi=1. c_Arrow__Order__Mirabelle_OProf=1. c_Arrow__Order__Mirabelle_Omkbot=1. c_Arrow__Order__Mirabelle_Omktop=1. v_a=1. v_Lab____=1. v_Lba____=1. v_h____=1. v_n____=1. t_a=1. v_F=1. v_a____=1. v_b____=1. v_c____=1. v_d____=1. v_e____=1. v_P____=1. c_Arrow__Order__Mirabelle_Oabove=1. hAPP=1. tc_fun=1. tc_prod=1. c_Nat_Osemiring__1__class_Oof__nat=1. c_Finite__Set_Ocard=1. c_Hilbert__Choice_OEps=1. c_SetInterval_Oord__class_OgreaterThan=1. c_SetInterval_Oord__class_OlessThan=1. v_sko__Arrow__Order__Mirabelle__Xdictator__def__1=1. c_The=1. c_List_Osko__List__Xall__nat__less__eq__1__2=1. c_List_Osko__List__Xex__nat__less__eq__1__1=1. c_lessequals=1. c_HOL_Oord__class_Oless=1. c_HOL_Oplus__class_Oplus=1. c_HOL_Ozero__class_Ozero=1. c_Suc=1. c_HOL_Ominus__class_Ominus=1. c_in=1. c_HOL_Oone__class_Oone=1. c_Orderings_Obot__class_Obot=1. c_Orderings_Otop__class_Otop=1. c_HOL_Ouminus__class_Ouminus=1. c_HOL_OIf=1. c_fequal=1. c_FunDef_OTHE__default=1. c_List_Olist_ONil=1. c_ATP__Linkup_Osko__Nat__Xinfinite__descent__1__1=1. c_ATP__Linkup_Osko__Nat__Xnat__less__induct__1__1=1. c_Lattices_Olower__semilattice__class_Oinf=1. c_Power_Opower__class_Opower=1. c_List_Olist_OCons=1. c_ATP__Linkup_Osko__Nat__Xinfinite__descent__measure__1__1=1. c_ATP__Linkup_Osko__Nat__Xmeasure__induct__1__1=1. c_ATP__Linkup_Osko__Nat__Xmeasure__induct__rule__1__1=1. c_COMBC=1. c_COMBB=1. c_Pair=1. c_Set_Ovimage=1. c_Finite__Set_Osetsum=1. c_Finite__Set_Osetprod=1. c_FuncSet_OPi=1. c_List_Osko__List__Xfoldl__apply__inv__1__1=1. c_ATP__Linkup_Osko__FunDef__Xfundef__default__value__1__1=1. c_COMBS=1. c_List_Ofoldl=1. c_ATP__Linkup_Osko__FunDef__Xfundef__ex1__iff__1__1=1. c_Fun_Ooverride__on=1. c_ATP__Linkup_Osko__FunDef__Xfundef__ex1__existence__1__1=1. c_ATP__Linkup_Osko__FunDef__Xfundef__ex1__uniqueness__1__1=1.
% 2.96/3.29
% 2.96/3.29 ============================== end of process initial clauses ========
% 2.96/3.29
% 2.96/3.29 ============================== CLAUSES FOR SEARCH ====================
% 2.96/3.29
% 2.96/3.29 ============================== end of clauses for search =============
% 2.96/3.29
% 2.96/3.29 ============================== SEARCH ================================
% 2.96/3.29
% 2.96/3.29 % Starting search at 0.73 seconds.
% 2.96/3.29
% 2.96/3.29 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 32 (0.00 of 1.21 sec).
% 2.96/3.29
% 2.96/3.29 Low Water (keep): wt=103.000, iters=3815
% 2.96/3.29
% 2.96/3.29 Low Water (keep): wt=71.000, iters=3470
% 2.96/3.29
% 2.96/3.29 Low Water (keep): wt=68.000, iters=3420
% 2.96/3.29
% 2.96/3.29 Low Water (keep): wt=61.000, iters=3372
% 2.96/3.29
% 2.96/3.29 Low Water (keep): wt=59.000, iters=3521
% 2.96/3.29
% 2.96/3.29 Low Water (keep): wt=53.000, iters=3353
% 2.96/3.29
% 2.96/3.29 Low Water (keep): wt=51.000, iters=3337
% 2.96/3.29
% 2.96/3.29 Low Water (keep): wt=48.000, iters=3348
% 2.96/3.29
% 2.96/3.29 Low Water (keep): wt=46.000, iters=3357
% 2.96/3.29
% 2.96/3.29 Low Water (keep): wt=44.000, iters=3340
% 2.96/3.29
% 2.96/3.29 Low Water (keep): wt=43.000, iters=3348
% 2.96/3.29
% 2.96/3.29 Low Water (keep): wt=42.000, iters=3341
% 2.96/3.29
% 2.96/3.29 Low Water (keep): wt=41.000, iters=3371
% 2.96/3.29
% 2.96/3.29 Low Water (keep): wt=40.000, iters=3386
% 2.96/3.29
% 2.96/3.29 Low Water (keep): wt=39.000, iters=3387
% 2.96/3.29
% 2.96/3.29 Low Water (keep): wt=38.000, iters=3367
% 2.96/3.29
% 2.96/3.29 Low Water (keep): wt=37.000, iters=3397
% 2.96/3.29
% 2.96/3.29 Low Water (keep): wt=36.000, iters=3453
% 2.96/3.29
% 2.96/3.29 Low Water (keep): wt=34.000, iters=3451
% 2.96/3.29
% 2.96/3.29 Low Water (keep): wt=33.000, iters=3405
% 2.96/3.29
% 2.96/3.29 Low Water (keep): wt=31.000, iters=3345
% 2.96/3.29
% 2.96/3.29 Low Water (keep): wt=30.000, iters=3450
% 2.96/3.29
% 2.96/3.29 Low Water (keep): wt=29.000, iters=3393
% 2.96/3.29
% 2.96/3.29 Low Water (keep): wt=28.000, iters=3406
% 2.96/3.29
% 2.96/3.29 Low Water (keep): wt=27.000, iters=3345
% 2.96/3.29
% 2.96/3.29 Low Water (keep): wt=26.000, iters=3396
% 2.96/3.29
% 2.96/3.29 Low Water (keep): wt=25.000, iters=3474
% 2.96/3.29
% 2.96/3.29 Low Water (keep): wt=24.000, iters=3468
% 2.96/3.29
% 2.96/3.29 Low Water (keep): wt=22.000, iters=3435
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% 2.96/3.29 Low Water (keep): wt=21.000, iters=3396
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% 2.96/3.29 Low Water (keep): wt=20.000, iters=3535
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% 2.96/3.29 Low Water (keep): wt=17.000, iters=3394
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% 2.96/3.29 Low Water (keep): wt=16.000, iters=3336
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% 2.96/3.29 Low Water (keep): wt=14.000, iters=3333
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% 2.96/3.29 Low Water (displace): id=3866, wt=197.000
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% 2.96/3.29 Low Water (displace): id=2553, wt=195.000
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% 2.96/3.29 Low Water (displace): id=2552, wt=193.000
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% 2.96/3.29 Low Water (displace): id=2549, wt=190.000
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% 2.96/3.29 Low Water (displace): id=2560, wt=189.000
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% 2.96/3.29 Low Water (displace): id=4247, wt=188.000
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% 2.96/3.29 Low Water (displace): id=2554, wt=183.000
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% 2.96/3.29 Low Water (displace): id=2558, wt=170.000
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% 2.96/3.29 Low Water (displace): id=4233, wt=155.000
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% 2.96/3.29 Low Water (displace): id=4239, wt=151.000
% 5.57/5.89
% 5.57/5.89 Low Water (displace): id=4242, wt=148.000
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% 5.57/5.89 Low Water (displace): id=4240, wt=141.000
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% 5.57/5.89 Low Water (displace): id=3709, wt=139.000
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% 5.57/5.89 Low Water (displace): id=3703, wt=135.000
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% 5.57/5.89 Low Water (displace): id=3712, wt=128.000
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% 5.57/5.89 Low Water (displace): id=3955, wt=126.000
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% 5.57/5.89 Low Water (displace): id=3956, wt=122.000
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% 5.57/5.89 Low Water (displace): id=4237, wt=119.000
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% 5.57/5.89 Low Water (displace): id=3146, wt=117.000
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% 5.57/5.89 Low Water (displace): id=4251, wt=116.000
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% 5.57/5.89 Low Water (displace): id=3941, wt=104.000
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% 5.57/5.89 Low Water (displace): id=4257, wt=103.000
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% 5.57/5.89 Low Water (displace): id=4484, wt=102.000
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% 5.57/5.89 Low Water (displace): id=2512, wt=101.000
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% 5.57/5.89 Low Water (displace): id=2516, wt=100.000
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% 5.57/5.89 Low Water (displace): id=4236, wt=99.000
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% 5.57/5.89 Low Water (displace): id=4256, wt=96.000
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% 5.57/5.89 Low Water (displace): id=4511, wt=86.000
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% 5.57/5.89 Low Water (displace): id=3971, wt=85.000
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% 5.57/5.89 Low Water (displace): id=3969, wt=84.000
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% 5.57/5.89 Low Water (displace): id=3967, wt=83.000
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% 5.57/5.89 Low Water (displace): id=3946, wt=82.000
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% 5.57/5.89 Low Water (displace): id=3973, wt=81.000
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% 5.57/5.89 Low Water (displace): id=2780, wt=78.000
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% 5.57/5.89 Low Water (displace): id=4510, wt=69.000
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% 5.57/5.89 Low Water (displace): id=3961, wt=68.000
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% 5.57/5.89 Low Water (displace): id=3364, wt=67.000
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% 5.57/5.89 Low Water (displace): id=4048, wt=66.000
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% 5.57/5.89 Low Water (displace): id=11467, wt=52.000
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% 5.57/5.89 Low Water (displace): id=6241, wt=51.000
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% 5.57/5.89 Low Water (displace): id=7367, wt=50.000
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% 5.57/5.89 Low Water (displace): id=12909, wt=49.000
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% 5.57/5.89 Low Water (displace): id=11329, wt=48.000
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% 5.57/5.89 Low Water (displace): id=10359, wt=47.000
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% 5.57/5.89 Low Water (displace): id=12675, wt=45.000
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% 5.57/5.89 Low Water (displace): id=13111, wt=44.000
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% 5.57/5.89 Low Water (displace): id=13159, wt=43.000
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% 5.57/5.89 Low Water (displace): id=12414, wt=42.000
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% 5.57/5.89 Low Water (displace): id=13083, wt=41.000
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% 5.57/5.89 Low Water (displace): id=13633, wt=13.000
% 5.57/5.89
% 5.57/5.89 ============================== PROOF =================================
% 5.57/5.89 % SZS status Unsatisfiable
% 5.57/5.89 % SZS output start Refutation
% 5.57/5.89
% 5.57/5.89 % Proof 1 at 4.46 (+ 0.10) seconds.
% 5.57/5.89 % Length of proof is 57.
% 5.57/5.89 % Level of proof is 15.
% 5.57/5.89 % Maximum clause weight is 26.000.
% 5.57/5.89 % Given clauses 3263.
% 5.57/5.89
% 5.57/5.89 1 class_Ring__and__Field_Ocomm__semiring__1(tc_nat) # label(clsarity_nat__Ring__and__Field_Ocomm__semiring__1) # label(axiom). [assumption].
% 5.57/5.89 16 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Power_Opower__class_Opower(B,c_HOL_Ozero__class_Ozero(tc_nat),A) = c_HOL_Oone__class_Oone(A) # label(cls_class__semiring_Opwr__0_0) # label(axiom). [assumption].
% 5.57/5.89 101 class_Ring__and__Field_Ozero__neq__one(tc_nat) # label(clsarity_nat__Ring__and__Field_Ozero__neq__one) # label(axiom). [assumption].
% 5.57/5.89 102 -class_Ring__and__Field_Ozero__neq__one(A) | -class_Ring__and__Field_Ono__zero__divisors(A) | -class_Ring__and__Field_Omult__zero(A) | -class_Power_Opower(A) | c_Power_Opower__class_Opower(B,c_HOL_Ozero__class_Ozero(tc_nat),A) != c_HOL_Ozero__class_Ozero(A) # label(cls_power__eq__0__iff_1) # label(axiom). [assumption].
% 5.57/5.89 119 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,A) = c_Lattices_Olower__semilattice__class_Oinf(C,B,A) # label(cls_inf__commute_0) # label(axiom). [assumption].
% 5.57/5.89 133 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),c_Lattices_Olower__semilattice__class_Oinf(B,C,A)),C)) # label(cls_inf__le2_0) # label(axiom). [assumption].
% 5.57/5.89 136 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,B,A) = B # label(cls_inf__idem_0) # label(axiom). [assumption].
% 5.57/5.89 137 class_Lattices_Olower__semilattice(tc_nat) # label(clsarity_nat__Lattices_Olower__semilattice) # label(axiom). [assumption].
% 5.57/5.89 139 class_Orderings_Olinorder(tc_nat) # label(clsarity_nat__Orderings_Olinorder) # label(axiom). [assumption].
% 5.57/5.89 144 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) | hBOOL(hAPP(hAPP(c_lessequals(A),C),B)) # label(cls_not__leE_0) # label(axiom). [assumption].
% 5.57/5.89 147 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),C),B)) # label(cls_linorder__not__less_1) # label(axiom). [assumption].
% 5.57/5.89 193 c_Suc(A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat)) # label(cls_Suc__eq__plus1_0) # label(axiom). [assumption].
% 5.57/5.89 204 hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),A),B) = c_HOL_Ozero__class_Ozero(tc_nat) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)) # label(cls_diff__is__0__eq_1) # label(axiom). [assumption].
% 5.57/5.89 210 hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C)) # label(cls_nat__add__assoc_0) # label(axiom). [assumption].
% 5.57/5.89 270 -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Suc(B)),A)) # label(cls_not__less__eq__eq_1) # label(axiom). [assumption].
% 5.57/5.89 271 -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),c_HOL_Oone__class_Oone(tc_nat))),A)). [copy(270),rewrite([193(8)])].
% 5.57/5.89 305 hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),A) # label(cls_nat__add__commute_0) # label(axiom). [assumption].
% 5.57/5.89 327 hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),A),C)),B)) # label(cls_le__diff__conv_0) # label(axiom). [assumption].
% 5.57/5.89 399 A = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Ozero__class_Ozero(tc_nat)) # label(cls_natgb_Oadd__r0__iff_1) # label(axiom). [assumption].
% 5.57/5.89 400 hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Ozero__class_Ozero(tc_nat)) = A. [copy(399),flip(a)].
% 5.57/5.89 401 hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A) = A # label(cls_plus__nat_Oadd__0_0) # label(axiom). [assumption].
% 5.57/5.89 426 hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B))) # label(cls_le__add1_0) # label(axiom). [assumption].
% 5.57/5.89 679 hAPP(hAPP(c_COMBB(A,B,C,D),E),F) = hAPP(A,hAPP(E,F)) # label(cls_COMBB__def_0) # label(axiom). [assumption].
% 5.57/5.89 681 hAPP(c_COMBS(A,B,C,D,E),F) = hAPP(hAPP(A,F),hAPP(B,F)) # label(cls_COMBS__def_0) # label(axiom). [assumption].
% 5.57/5.89 694 class_Ring__and__Field_Ono__zero__divisors(tc_nat) # label(clsarity_nat__Ring__and__Field_Ono__zero__divisors) # label(axiom). [assumption].
% 5.57/5.89 696 class_Ring__and__Field_Omult__zero(tc_nat) # label(clsarity_nat__Ring__and__Field_Omult__zero) # label(axiom). [assumption].
% 5.57/5.89 701 class_Power_Opower(tc_nat) # label(clsarity_nat__Power_Opower) # label(axiom). [assumption].
% 5.57/5.89 727 c_Power_Opower__class_Opower(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Oone__class_Oone(tc_nat). [resolve(1,a,16,a)].
% 5.57/5.89 791 -class_Ring__and__Field_Ono__zero__divisors(tc_nat) | -class_Ring__and__Field_Omult__zero(tc_nat) | -class_Power_Opower(tc_nat) | c_Power_Opower__class_Opower(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat). [resolve(101,a,102,a)].
% 5.57/5.89 792 c_HOL_Oone__class_Oone(tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat). [copy(791),rewrite([727(10)]),unit_del(a,694),unit_del(b,696),unit_del(c,701)].
% 5.57/5.89 823 c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(B,A,tc_nat). [resolve(137,a,119,a)].
% 5.57/5.89 834 hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat)),B)). [resolve(137,a,133,a)].
% 5.57/5.89 837 c_Lattices_Olower__semilattice__class_Oinf(A,A,tc_nat) = A. [resolve(137,a,136,a)].
% 5.57/5.89 858 hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B)) | hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),A)). [resolve(139,a,144,a)].
% 5.57/5.89 860 -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),A)). [resolve(139,a,147,a)].
% 5.57/5.89 907 c_HOL_Oone__class_Oone(tc_nat) = c_0. [new_symbol(792)].
% 5.57/5.89 976 -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),c_0)),A)). [back_rewrite(271),rewrite([907(12)])].
% 5.57/5.89 1283 hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),A),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B)))). [resolve(426,a,327,b),rewrite([210(15)])].
% 5.57/5.89 3496 hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat)),B) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(834,a,204,b)].
% 5.57/5.89 4712 -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_0),B))),A)). [resolve(976,b,426,a),rewrite([210(11)])].
% 5.57/5.89 5468 -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(c_COMBS(c_HOL_Oplus__class_Oplus(tc_nat),B,C,D,E),c_0))),A)). [para(681(a,2),4712(a,1,1,2,2))].
% 5.57/5.89 6689 -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(c_COMBS(c_HOL_Oplus__class_Oplus(tc_nat),A,B,C,D),c_0)),E)),E)). [para(305(a,1),5468(a,1,1,2))].
% 5.57/5.89 7070 hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(c_COMBS(c_HOL_Oplus__class_Oplus(tc_nat),B,C,D,E),c_0)),A))). [resolve(6689,a,858,b)].
% 5.57/5.89 18587 -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),A),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B))),A)). [resolve(1283,a,860,b)].
% 5.57/5.89 18622 -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_nat))). [para(3496(a,1),18587(a,1,1,2,1,2)),rewrite([401(12),823(9)])].
% 5.57/5.89 18626 -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(c_COMBS(c_HOL_Oplus__class_Oplus(tc_nat),A,B,C,D),E)),c_Lattices_Olower__semilattice__class_Oinf(F,hAPP(A,E),tc_nat))). [para(681(a,2),18622(a,1,1,2)),rewrite([823(10)])].
% 5.57/5.89 18765 -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(B,A))),c_Lattices_Olower__semilattice__class_Oinf(C,hAPP(B,A),tc_nat))). [para(681(a,1),18626(a,1,1,2))].
% 5.57/5.89 18823 -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(A,c_HOL_Ozero__class_Ozero(tc_nat))),c_Lattices_Olower__semilattice__class_Oinf(B,hAPP(A,c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat))). [para(401(a,1),18765(a,1,1,2))].
% 5.57/5.89 18869 -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(A,hAPP(B,c_HOL_Ozero__class_Ozero(tc_nat)))),c_Lattices_Olower__semilattice__class_Oinf(C,hAPP(A,hAPP(B,c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat))). [para(679(a,1),18823(a,1,1,2)),rewrite([679(12)])].
% 5.57/5.89 18983 -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(A,B)),c_Lattices_Olower__semilattice__class_Oinf(C,hAPP(A,B),tc_nat))). [para(305(a,1),18869(a,1,1,2,2)),rewrite([401(8),400(10)])].
% 5.57/5.89 18993 -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(A,B),hAPP(C,B))),c_Lattices_Olower__semilattice__class_Oinf(D,hAPP(c_COMBS(A,C,E,F,V6),B),tc_nat))). [para(681(a,1),18983(a,1,1,2))].
% 5.57/5.89 19956 -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(A,B),hAPP(C,B))),hAPP(c_COMBS(A,C,D,E,F),B))). [para(837(a,1),18993(a,1,2))].
% 5.57/5.89 20050 -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(c_COMBS(A,B,C,D,E),F)),hAPP(c_COMBS(A,B,V6,V7,V8),F))). [para(681(a,2),19956(a,1,1,2))].
% 5.57/5.89 20118 -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(c_COMBS(A,B,C,D,E),F)),hAPP(hAPP(A,F),hAPP(B,F)))). [para(681(a,1),20050(a,1,2))].
% 5.57/5.89 20136 -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(c_COMBS(A,hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),B,C,D),E)),hAPP(hAPP(A,E),E))). [para(401(a,1),20118(a,1,2,2))].
% 5.57/5.89 20417 -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(c_COMBS(c_COMBB(A,B,C,D),hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),E,F,V6),V7)),hAPP(A,hAPP(V7,V7)))). [para(679(a,1),20136(a,1,2))].
% 5.57/5.89 20418 $F. [resolve(20417,a,7070,a)].
% 5.57/5.89
% 5.57/5.89 % SZS output end Refutation
% 5.57/5.89 ============================== end of proof ==========================
% 5.57/5.89
% 5.57/5.89 ============================== STATISTICS ============================
% 5.57/5.89
% 5.57/5.89 Given=3263. Generated=174300. Kept=20080. proofs=1.
% 5.57/5.89 Usable=3247. Sos=9998. Demods=390. Limbo=13, Disabled=7792. Hints=0.
% 5.57/5.89 Megabytes=34.37.
% 5.57/5.89 User_CPU=4.46, System_CPU=0.10, Wall_clock=4.
% 5.57/5.89
% 5.57/5.89 ============================== end of statistics =====================
% 5.57/5.89
% 5.57/5.89 ============================== end of search =========================
% 5.57/5.89
% 5.57/5.89 THEOREM PROVED
% 5.57/5.89 % SZS status Unsatisfiable
% 5.57/5.89
% 5.57/5.89 Exiting with 1 proof.
% 5.57/5.89
% 5.57/5.89 Process 27039 exit (max_proofs) Fri Jul 1 23:18:43 2022
% 5.57/5.89 Prover9 interrupted
%------------------------------------------------------------------------------